The Hammers collected their fourth point of the season as they and the Magpies drew a blank at St James' Park.
Downing told the club's official website: "I enjoyed and I certainly thought we could have won the game with the chances we had. I think we played good counter-attacking football and certainly had chances to win it.
"It was always going to be difficult going to Newcastle for their first home game but we got a result and I think we did really well."
Downing made his first start for the Hammers against Alan Pardew's side following his £6m move from Liverpool.